Abstract.---The use of comparative methods to test evolutionary hypotheses has become more common at both the macro- and microevolutionary levels. The application of such techniques is especially troublesome at the interface of these levels because phylogenetic relationships are often difficult to estimate. The use of a technique developed to estimate intraspecific cladograms combined with more traditional methods of phylogenetic estimation can improve the estimate in data sets containing a range of diversity when the lower bound of the range approaches 0% divergence. For nucleotide sequence data from the 16S region of the mitochondrial DNA from 72 individuals representing 37 species, this combined-procedures approach improved the estimate of phylogenetic relationships using maximum-parsimony, maximum-likelihood, and neighbor-joining methods. The estimated trees were used to examine systematic hypotheses relating to the crayfish genus Orconectes and species relationships within the subgenus Procericambarus. The monophyly of Procericambarus is not supported by the mitochondrial data, and the hypotheses of unique origins of various morphological features previously used in determining crayfish relationships is unsupported.
[Crayfish; mitochondrial DNA; molecular systematics; parsimony; phylogeny reconstruction; Orconectes.]

Abstract.---We examined the statistical performance (in terms of type I error rates) of Felsenstein's (1985, Am. Nat. 125:1--15) comparative method of phylogenetically independent contrasts for testing hypotheses about evolutionary correlations of continuous-valued characters. We simulated data along two different phylogenies, one for 15 species of plethodontid salamanders and the other for 49 species of Carnivora and ungulates. We implemented 15 different models of character evolution, 14 of which deviated from Brownian motion, which is in effect assumed by the method. The models studied included the Ornstein--Uhlenbeck process and punctuated equilibrium (change allowed in only one daughter at each bifurcation) both with and without trends and limits on how far phenotypes could evolve. As has been shown in several previous simulation studies, a nonphylogenetic Pearson correlation of species' mean values yielded inflated type I error rates under most models, including that of simple Brownian motion. Independent contrasts yielded acceptable type I error rates under Brownian motion (and in preliminary studies under slight deviations from this model), but they were inflated under most other models. This new result confirms the model dependence of independent contrasts. However, when branch lengths were checked and transformed, then type I error rates of independent contrasts were reduced. Moreover, the maximum observed type I error rates never exceeded twice the nominal P value at a = 0.05. In comparison, the nonphylogenetic correlation tended to yield extremely inflated (and highly variable) type I error rates. These results constitute another demonstration of the general superiority of phylogenetically based statistical methods over nonphylogenetic ones, even under extreme deviations from a Brownian motion model. These results also show the necessity of checking the assumptions of statistical comparative methods and indicate that diagnostic checks and remedial measures can substantially improve the performance of the independent contrasts method.
[Comparative method; computer simulation;independent contrasts; phylogeny; hypothesis testing; statistics; correlated evolution.]

Abstract.---The correlation that exists among multiple cladograms is often taken as evidence of some underlying macroevolutionary phenomenon common to the histories of those clades and, thus, as an explanation of the patterns of association of the constituent taxa. Such studies have various forms, the most common of which are cladistic biogeography and host--parasite coevolution. The issue of confidence has periodically been a theoretical consideration of vicariance biogeographers but in practice has been largely ignored by others. Previous approaches to assessing confidence in historical associations are examined here in relation to the difference between simple-event and cumulative probabilities and in relation to the restrictiveness of joint hypothesis testing. The phylogenetic covariance probability (PCP) test, a novel approach to assessing confidence in hypotheses of historical association, employs the empirical protocol of Brooks parsimony analysis (BPA) in an iterative, computer-intensive randomization routine. The PCP value consists of the frequency with which a solution as efficient or more efficient than the observed hypothesis of correlated phylogeny is achieved with random associations (e.g., of parasites and hosts or of taxa and areas). Because only the associations, and not the contributing phylogenies, are subjected to randomization, the test is not prone to certain criticisms leveled at other cladistic randomization routines. The behavior of the PCP test is examined in relation to eight published studies of historical association. This test is appropriately sensitive to the degrees of freedom allowed by the number of contributing clades and the number of taxa in those clades, to the extent of noncorrelated associations in the observed hypothesis, and to the relative information content contributing to that hypothesis.
[Biogeography; BPA; coevolution; confidence; historical associations; randomization.]

Abstract.---Finite mixture coding (FMC) is a new method of coding continuous characters. FMC uses a three-step goodness-of-fit procedure to assign codes. First, for a given measurement, parameters are estimated for a number of density functions that describe a data set either of species means or of measurements of specimens from several species. The density functions represent either a single population or a mixture of populations (e.g., a mixture of two normal distributions). Next, a goodness-of-fit criterion (the Akaike information criterion) is used to determine which of the density functions best describes the data set. The best function indicates the number of populations into which the variates of the data set can be segregated. Finally, species are assigned to the population for which its probability of membership is highest. Each population is then assigned a code, and species falling within the same population share the same code. Although other coding methods incorporate statistical tests or parameters into the coding process, FMC is the only method that produces codes as the direct output of a statistical procedure.
[Code; continuous character; finite mixture analysis; likelihood estimation; cladistics.]

Abstract.---The method of minimum evolution was introduced by Edwards and Cavalli-Sforza (1963, Heredity 18:553, Ann. Hum. Genet. 27:104--105) for the reconstruction of phylogenetic trees. Its relationship to the subsequently developed parsimony methods and the logical basis of the methods are discussed, with special reference to probability models. The minimum evolution method did not derive from Hennig's phylogenetic systematics but rather as an approximation to the maximum-likelihood solution for a model of random evolution.
[Phylogenetic trees; minimum evolution; Darwin principle; Ockham's razor; parsimony.]

Abstract.---Molecular data are commonly used to reconstruct the evolutionary histories of organisms. However, evolutionary reconstructions from different molecular data sets sometimes conflict. It is generally unknown whether these different estimates of history result from random variation in the processes of nucleotide substitution or from fundamentally different evolutionary mechanisms underlying the histories of the genes analyzed. We describe a novel likelihood ratio test that compares different topologies (each estimated from a different data partition for the same taxa) to determine if they are significantly different. The results of this test indicate that different genes provide significantly different phylogenies for amniotes, supporting earlier suggestions based on less direct tests. These results suggest that some molecular data can give misleading information about evolutionary history.
[Likelihood ratio test; maximum likelihood; phylogenetic methods; phylogenetic heterogeneity.]

Abstract.---Several recent studies have included attempts to use the balance of phylogenetic trees, i.e., the extent to which sister groups within a tree tend to be the same size, to test hypotheses about the macroevolutionary processes that produced them. Such tests require measures of balance or imbalance and the moments or probability distributions of these measures under some null models. In earlier work, I developed recursion equations for the mean, variance, skewness, and complete probability distribution of Colless's coefficient of imbalance (I) (Rogers, 1994, Evolution 48:2026--2036). In this paper, I report the extension of these techniques to two additional imbalance measures, the number of unbalanced nodes on a tree (J) and Sackin's index (K), under both the equal-rates Markov (ERM) model and the equal probability (EP) model. I also show how to find the correlations and joint probability distributions of all pairs of these three coefficients. I and K are so highly correlated for trees of all sizes that K contains little additional information about tree balance that is not conveyed by I. The correlation of I and J, however, decreases rapidly with increasing tree size, indicating that the testing of macroevolutionary hypotheses may be refined by employing the joint distribution of these two coefficients. The results of two simulation studies of non-ERM speciation processes are used to illustrate how the joint distribution of I and J may be used.
[Phylogenetic trees; macroevolutionary processes; speciation; tree imbalance coefficients; probability distributions.]